Probability Test 1 Fall 2023

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 and 1.

Front

What is the formula for calculating the probability of an event?

Back

P(A) = Number of favorable outcomes / Total number of outcomes.

Front

Define conditional probability.

Back

Conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(A|B).

Front

What is the formula for conditional probability?

Back

P(A|B) = P(A and B) / P(B) if P(B) > 0.

Front

What does it mean if two events are independent?

Back

Two events are independent if the occurrence of one event does not affect the probability of the other event.

Front

How do you calculate the probability of independent events occurring together?

Back

P(A and B) = P(A) * P(B).

Front

What is the complement of an event?

Back

The complement of an event A is the event that A does not occur, denoted as A'. The probability of the complement is P(A') = 1 - P(A).

Front

What is Bayes' Theorem?

Back

Bayes' Theorem relates the conditional and marginal probabilities of random events, expressed as P(A|B) = [P(B|A) * P(A)] / P(B).

Front

What is the law of total probability?

Back

The law of total probability states that if B1, B2, ..., Bn are disjoint events that cover the sample space, then P(A) = Σ P(A|Bi) * P(Bi).

Front

Define joint probability.

Back

Joint probability is the probability of two events occurring together, denoted as P(A and B).